# Data-driven Discovery of Digital Twins in Biomedical Research

arXiv: https://arxiv.org/abs/2508.21484 · HTML: https://mlsanity.com/paper/2508.21484/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 95 of its 229 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 30 of 95)

- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Extracting Sparse High-Dimensional Dynamics from Limited Data](https://mlsanity.com/paper/1707.08528/) (2017)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)

## Built on by (most cited first, 2 of 2)

- [Position: Biology is the Challenge Physics-Informed ML Needs to Evolve](https://mlsanity.com/paper/2510.25368/) (2025)
- [A Temporal Machine Learning-Based Time-to-Event Model for Predicting ALS Progression and Healthcare Utilization](https://mlsanity.com/paper/2607.14190/) (2026)

## Abstract (arXiv)

Recent technological advances have expanded the availability of high-throughput biological datasets, enabling the reliable design of digital twins of biomedical systems or patients. Such computational tools represent key reaction networks driving perturbation or drug response and can guide drug discovery and personalized therapeutics. Yet, their development still relies on laborious data integration by the human modeler, so that automated approaches are critically needed. The success of data-driven system discovery in Physics, rooted in clean datasets and well-defined governing laws, has fueled interest in applying similar techniques in Biology, which presents unique challenges. Here, we reviewed methodologies for automatically inferring digital twins from biological time series, which mostly involve symbolic or sparse regression. We evaluate algorithms according to eight biological and methodological challenges, associated to noisy/incomplete data, multiple conditions, prior knowledge integration, latent variables, high dimensionality, unobserved variable derivatives, candidate library design, and uncertainty quantification. Upon these criteria, sparse regression generally outperformed symbolic regression, particularly when using Bayesian frameworks. We further highlight the emerging role of deep learning and large language models, which enable innovative prior knowledge integration, though the reliability and consistency of such approaches must be improved. While no single method addresses all challenges, we argue that progress in learning digital twins will come from hybrid and modular frameworks combining chemical reaction network-based mechanistic grounding, Bayesian uncertainty quantification, and the generative and knowledge integration capacities of deep learning. To support their development, we further propose a benchmarking framework to evaluate methods across all challenges.